# Proportion and similarity question

Discussion in 'Community Discussion' started by Jasonbot, Nov 28, 2007.

1. ### Jasonbot macrumors 68020

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Aug 15, 2006
Location:
The Rainbow Nation RSA
#1

thanks,
Jason

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2. ### Jasonbot thread starter macrumors 68020

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Location:
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#2
Don't they teach geometry in foreign countries?

3. ### swiftaw macrumors 603

Joined:
Jan 31, 2005
Location:
Omaha, NE, USA
#3
OK,

BC^2 + BD^2 = CD^2

Putting these together we get that

AB^2 + CD^2 - BC^2 = AD^2 (*)

Now, by similarity we have that AC = 3AB, so AC^2 = 9AB^2.

Using that fact (*) becomes
(1/9)AC^2 + CD^2 - BC^2 = AD^2

But AC^2 = AD^2 + CD^2, thus

Re-arranging we get

Now, use the fact that CD^2 = AC^2 - AD^2 we get

or, in other words
2AD^2 = (10/9)AC^2 - BC^2 (**)

But, AC = (3/2)BC, so substituting into (**) gets us

2AD^2 = (10/9)(9/4)BC^2 - BC^2 = (6/4)BC^2

Doubling both sides

Taking square roots

4. ### Jasonbot thread starter macrumors 68020

Joined:
Aug 15, 2006
Location:
The Rainbow Nation RSA
#4
Thank you so much! I have no idea how you see these things but I'm sure Ill get it DO you look at what you're supposed to prove and work backwards?

5. ### swiftaw macrumors 603

Joined:
Jan 31, 2005
Location:
Omaha, NE, USA
#5
No, that is bad form. The only thing I looked in the final answer was that it only contained AD and BC. I started by writing down things I knew to be true and then tried to combine them in such a way to leave only AD and BC.